Problem: Solve for $x$ and $y$ using elimination. ${-3x-6y = -63}$ ${3x+5y = 53}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x-6y = -63}\thinspace$ to find $x$ ${-3x - 6}{(10)}{= -63}$ $-3x-60 = -63$ $-3x-60{+60} = -63{+60}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {3x+5y = 53}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(10)}{= 53}$ ${x = 1}$